Song performed for Decca audition and “Get Back” rehearsal sessions

What was the only song performed by the Beatles at their January 1, 1962 Decca audition, at their June 6, 1962 EMI commercial test and during the “Get Back” rehearsal sessions?
Bonus: What is the connection between that song and the Beatles February 1964 visit to Miami Beach?
The Beatles performed “Besame Mucho” at their January 1, 1962 Decca audition, at their June 6, 1962 EMI commercial test and during the “Get Back” rehearsal sessions. The song, written by Consuelo Valazquez and Sunny Skylar, was a Latin standard that came to the attention of the Beatles by way of the Coasters, who issued the song in two parts on the single Atco 6163 in 1960. On the night before their second Ed Sullivan Show appearance broadcast live from Miami Beach, the Beatles went to see the Coasters at a local Miami nightclub. The group included several Coasters songs in their club appearances during their formative years. At their Decca audition, the Beatles played two other Coasters’ songs, “Three Cool Cats” and “Searchin’.”
The Beatles performed three songs recorded by the Coasters at their January 1, 1962, Decca audition: Three Cool Cats, Searchin’ and Besame Mucho. The first two are on Anthology 1. The group’s rendition of Besame Mucho from their June 6, 1962, EMI commercial test is also on the album.